Related papers: On Bosonic Wightman Quantum Field Theories
We give introductions into the representation theory of the Virasoro algebra, Wightman axioms and vertex algebras in the first part. In the second part, we compare the above definitions. We give a proof of Luescher and Mack that a dilation…
The classical Weyl-von Neumann theorem states that for any self-adjoint operator $A$ in a separable Hilbert space $\mathfrak H$ there exists a (non-unique) Hilbert-Schmidt operator $C = C^*$ such that the perturbed operator $A+C$ has purely…
We consider the quantum-mechanical problem of a relativistic Dirac particle moving in the Coulomb field of a point charge $Ze$. In the literature, it is often declared that a quantum-mechanical description of such a system does not exist…
A new generalized Wick theorem for interacting fields in 2D conformal field theory is described. We briefly discuss its relation to the Borcherds identity and its derivation by an analytic method. Examples of the calculations of the…
Starting from bosonization, we study the operator that commute or commute up-to a total difference with of any quantized screen operator of a free field. We show that if there exists a operator in the form of a sum of two vertex operators…
We consider the general form of "Correlated Worldline" (CWL) theories of quantum gravity. We show that one can have 2 different kinds of CWL theory, in which the generating functional is written as either a sum or a product over multiple…
A boson mapping of pair field operators is presented. The mapping preserves all hermiticity properties and the Poisson bracket relations between fields and momenta. The most practical application of the boson mapping is to field theories…
There are essentially two different approaches to the axiomatization of quantum field theory (QFT): algebraic QFT, going back to Haag and Kastler, and functorial QFT, going back to Atiyah and Segal. More recently, based on ideas by Baez and…
We study self-adjoint extensions of operators which are the product of the multiplication operator by an analytic function and the analytic continuation in a strip. We compute the deficiency indices of the product operator for a wide class…
We construct the spectral decomposition of field operators in bosonic quantum field theory as a limit of a strongly continuous family of positive-operator-valued measure decompositions. The latter arise from integrals over families of…
The properties of infinite series in the Wick powers of a free field whose two-point correlation function has a singular infrared behavior and does not satisfy the positivity condition are investigated. If these series are defined on an…
The notion of quasi boundary triples and their Weyl functions from extension theory of symmetric operators is extended to the general framework of adjoint pairs of operators under minimal conditions on the boundary maps. With the help of…
Although the Hamiltonian in quantum physics has to be a linear operator, it is possible to make quantum systems behave as if their Hamiltonians contained antilinear (i.e., semilinear or conjugate-linear) terms. For any given quantum system,…
Linear response theory is concerned with the way in which a physical system reacts to a small change in the applied forces. Here we show that quantum mechanics in the Heisenberg representation can be understood as a linear response theory.…
We present the Heisenberg-picture approach to the quantum evolution of the scalar fields in an expanding FRW universe which incorporates relatively simply the initial quantum conditions such as the vacuum state, the thermal equilibrium…
Explicit realizations of quantum field theory (QFT) are admitted by a revision to the Wightman axioms for the vacuum expectation values (VEV) of fields. The technical development of QFT is expanded beyond positive functionals on *-algebras…
Three major misconceptions concerning quantized tachyon fields: the energy spectrum unbounded from below, the frame-dependent and unstable vacuum state, and the non-covariant commutation rules, are shown to be a result of misrepresenting…
In this paper we study quantum field theory in impulsive plane wave spacetimes. We first analyze the geodesics and the formation of conjugate planes in these spacetimes. The behaviors of the world function and the van Vleck determinant near…
The chiral kinetic theory of Weyl fermions with collisions in the presence of weak electric and magnetic fields is derived from quantum field theories. It is found that the side-jump terms in the perturbative solution of Wigner functions…
We analyze functional analytic aspects of axiomatic formulations of nonlocal and noncommutative quantum field theories. In particular, we completely clarify the relation between the asymptotic commutativity condition, which ensures the CPT…